It is a combination of both things in bjj. A bjj blackbelt definitely has to be able to roll. The only real exceptions are for old people, in which case you sort of ask yourself how they would deal with another old man. At some point, your physical attributes fail you and even a ton of knowledge is not going to make you competitive. We have a bb at my gym who is 60. I saw him go from purple to black, when I got there as a 30 year old white belt, he could tap me out despite weighing 130 pounds and being 57 years old. These days, he can't really roll with me if I went full speed, but he can keep in step with me if we just flow roll. He still taps out white belts of all shapes and sizes though.
In bjj, you really don't get to black belt without being able whup a minimum amount of ass. BUt there are blackbelts with red panels (which signifies a teaching bb) as opposed to the traditional black panel (a fighting bb).